PRISM is an isogeny-based digital signature whose security relies on the problem of computing large prime degree isogenies from a supersingular elliptic curve of unknown endomorphism ring. In this paper, we design SPIDER, a digital signature that builds on a sigma protocol which when given a supersingular elliptic curve E, proves the knowledge of an isogeny \(\phi : E\rightarrow E'\) of prime (or non smooth) degree d. SPIDER can hence be seen as a proof of knowledge of a PRISM signature. The latter observation allows us to combine SPIDER and PRISM to obtain an Identity-Based Signature (IBS) which we denote by SPIDER-IBS. SPIDER-IBS is the most efficient and the most compact isogeny-based IBS scheme, as all its predecessors are based on isogeny group actions.